As known by the person skilled in the art, certain space observation missions require observation instruments furnished with a reflector (generally of so-called primary type) of large diameter. Such is notably the case for missions intended to observe the Earth or the sky with a high resolution from high geostationary orbits (“GEO”), Molnya or L2, for example. The future JWST (“James Webb Space Telescope”) telescope is one example. It actually uses a primary mirror about 6 meters in diameter.
The spacecraft that support such observation instruments are placed in orbit by means of rockets, the diameter of whose shroud fixes the diameter of the instrument. If the diameter of the instrument once in orbit exceeds that of the shroud, its primary reflector must be compacted (or folded back) by means of an appropriate mechanism during the firing phase (or launch phase), then decompacted (or deployed, or else unfolded) once in orbit by virtue of the mechanism and a decompacting strategy. These compacting/decompacting strategies are formulated under several constraints, such as for example mechanical constraints (related to the mechanisms), thermoelastic constraints and image-quality constraints. These constraints being well known, the number of solutions that can be implemented is relatively limited.
A solution, used notably for the JWST telescope, consists in using a primary mirror furnished with a central part and with at least two lateral parts folded back during firing. The central part and lateral parts consist for example of reflecting tiles of hexagonal shape which, once decompacted (or deployed), constitute a hexagonal tiling approximating a paraboloid. It is recalled that the hexagonal tiling is optimal because of the fact that it is 13.4% less dense than a rectangular tiling for one and the same limited band function on a circular domain.
This hexagonal tiling poses a problem because of the fact that it does not optimize the collecting (or reflecting) area. Specifically, if it is considered that the minimum collecting area is inscribed within a circular domain which does not include the entirety of the areas of the hexagonal collecting tiles, then all the portions of the tiles which are situated outside of this circular domain are useless and increase the footprint and the mass of the mirror. For example, it is possible to show that in the case of a tiling (sampling) comprising 7 hexagons, about 44.7% of the collecting area is useless because of the fact that it is outside of the disk to be approximated. If it is now considered that the entirety of the collecting area (and therefore of the areas of the tiles) must be subtended by a circular domain, then an anisotropy of the MTF (“Modulation Transfer Function”) is produced on account of the existence of unfilled domains on the periphery of the circle, and therefore of a deficit of collecting area.
To remedy this drawback it is possible for example to use smaller, and therefore a larger number of, hexagons. The approximation of the disk is indeed better and the lost collecting area smaller (about 22% of area lost in the presence of 37 hexagons). Alas, this solution considerably increases the difficulty of making the mirror. Specifically, since each hexagonal tile of the mirror has to be controlled actively by means of an actuator so as to counteract the instabilities in orbit, it is preferable to limit the number of actuators, notably to limit the rate of faults in orbit, the mechanical complexity of the support, deployment and orbit-control structure, the mass of the whole and the manufacturing cost.